Related papers: The Haar measure in solid mechanics
In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…
Thick adhesive layers have potential structural application in ship construction for the joining of a composite superstructure to a steel hull. The purpose of this study is to develop a mechanics model for the adhesive fracture of such lap…
Machine learning has found its way into almost every area of science and engineering, and we are only at the beginning of its exploration across fields. Being a popular, versatile and powerful framework, machine learning has proven most…
In this article I present the motivation for introducing the invariant functions of mass matrices, based on my own work, and give some examples. Since their introduction in 1985, in the framework of the standard electroweak model, they have…
Motivated by the Cauchy--Szeg\H{o} projections on a broad class of Siegel domains and the geometric quotient structures of nilpotent Lie groups observed by Nagel, Ricci, and Stein, we develop a martingale and Haar wavelet framework for…
Recently, there is interest in coincident 'sharpening' and 'learnability' transitions in monitored quantum systems. In the latter, an outside observer's ability to infer properties of a quantum system from measurements undergoes a phase…
Recently, the so-called Hermite-Hadamard inequality for (operator) convex functions with one variable has known extensive several developments by virtue of its nice properties and various applications. The fundamental target of this paper…
In the last decade, Human Activity Recognition (HAR) has become a vibrant research area, especially due to the spread of electronic devices such as smartphones, smartwatches and video cameras present in our daily lives. In addition, the…
We introduce the Statistical Asynchronous Regression (SAR) method: a technique for determining a relationship between two time varying quantities without simultaneous measurements of both quantities. We require that there is a time…
Quantifying coherence has received increasing attention, and considerable work has been directed towards finding coherence measures. While various coherence measures have been proposed in theory, an important issue following is how to…
This article discusses and explains the Hamiltonian formulation for a class of simple gauge invariant mechanical systems consisting of point masses and idealized rods. The study of these models may be helpful to advanced undergraduate or…
This thesis consists of two parts, connected by one central theme: the dynamics of the "shape of space". The first part of the thesis concerns the construction of a theory of gravity dynamically equivalent to general relativity (GR) in 3+1…
Motion capture systems, used across various domains, make body representations concrete through technical processes. We argue that the measurement of bodies and the validation of measurements for motion capture systems can be understood as…
(I.) We consider generalizations of an iterated function system and the associated Markov operators. A Markov operator, defined on the space of (deficient) topological measures on a locally compact space, is an infinite convex linear…
The specialised uses of solid angles mean that they are quite unfamiliar quantities. This article, apart from making solid angles a little more familiar, brings out several topics of general interest, such as how units are interrelated and…
We revisit the study of the mass functions and the bias of dark matter halos. Focusing on the limit of rare massive halos, we point out that exact analytical results can be obtained for the large-mass tail of the halo mass function. This is…
Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several…
We present an orthogonal expansion for real, function-regulated, second-order random measures over $\mathbb{R}^{d}$ with measure covariance. Such a expansion, which can be seen as a Karhunen-Lo\`eve decomposition, consists in a series of…
We study the matter bispectrum of large-scale structure by comparing the predictions of different perturbative and phenomenological models with the full three-dimensional bispectrum from $N$-body simulations estimated using modal methods.…
We provide a set of general tools for studying the alignments of dark matter halos and galaxies with respect to the large scale structure. The statistics of the positioning of these objects is represented by a Probability Distribution…